Stability of initialization response of fractional oscillators

Abstract

Application of fractional calculus representations, shortly termed as fractional constitute relations becomes an effective and powerful technique to characterize the rheological behavior of viscoelastic materials. Research on fractional oscillators provides a novel approach to deal with viscoelastically damped structures. This paper firstly investigates the memory effects or historical effects on dynamical responses of fractional oscillators via numerical simulations. Then the stability of initialization response is proved based on the unit impulse response function and the Lyapunov stability theorem for fractional differential equations. The main conclusion in this paper is that the stability of initialization responses of fractional oscillators is irrelevant to initial conditions or prehistory.